Borehole imaging

ABSTRACT

Method of detecting significant events intersecting a borehole from an image of the borehole wall comprising (a) converting the image into a three-dimensional orientation space; (b) selecting a parameter relation that represents the intersection of an event ( 3, 5  and  6 ) with the borehole wall; (c) creating a parameter space consisting of numbers as a function of the parameters, wherein each number is a measure of the support in the orientation space for an event characterized by the parameters that pertain to that number; (d) selecting in the parameter space a set of the largest numbers, wherein the parameters that pertain to each of these largest numbers represent the intersections of the significant events with the borehole wall; and (e) presenting the intersections pertaining to the set of the largest numbers as a list of data representing significant events.

[0001] The present invention relates to detecting significant eventsintersecting a borehole from an image of the borehole wall. In thespecification and in the claims, the word ‘borehole’ is used to refer toa borehole drilled in an underground formation, and examples of suchevents are fractures and bedding planes, which bedding planes are theinterfaces between formation layers. In general these events will beplanar on the scale of the borehole.

[0002] The image of the wall of the borehole comprises a two-dimensionalarray of numbers, each number being the magnitude of a relevant boreholeparameter at a point on the borehole wall. In the image, theco-ordinates of the point are given by the circumferential direction andthe depth along the borehole. A tilted planar event intersecting acylindrical borehole wall is shown on the image as a sinusoidal line.

[0003] The image is used for sedimentological and structural geologicalinterpretation of the formation around the borehole. In this imagerelevant events have to be distinguished from the intersections shown inthe image, this is normally done manually, however several automaticprocedures have also been developed in the industry. These are generallybased on variants of dip-meter algorithms, that determinecross-correlations of the button signals of the dip-meter in order toestablish the orientation of formation layers intersecting the boreholewall. Dipmeter algorithms, however, are most suited to determinecontinuous or slowly varying bedding dips, but they are not capable ofdetecting intersecting planar events or single thin events that have anorientation that significantly deviates from the bedding orientation.For this reason, dipmeter algorithms are not useful to detect fracturesin borehole images and the development of automatic procedures forfracture detection is an active area of research.

[0004] Such an image can be obtained by employing an acoustic tool, suchas the Ultrasonic Borehole Imager (UBI) tool available from Schlumbergeror the Circumferential Borehole imaging Logging (CBIL) tool availablefrom Baker. These tools obtain an image from the borehole wall byemitting a focused beam of highfrequency acoustic energy towards theborehole wall, followed by a series of measurements on the signal thatis reflected back from the borehole wall. Such an image can also beobtained by employing a microresistivity tool such as the Fullbore MicroImager or the Formation Micro Scanner available from Schlumberger. Themicroresistivity tool comprises a number of pads with individualelectrodes, which pads are during normal operation in contact with theborehole wall. The image can also be obtained by employing any othersuitable tool.

[0005] U.S. Pat. No. 5,960,371 specification discloses a method ofdetecting significant planar events intersecting a borehole from animage of the borehole wall, which image comprises a two-dimensionalarray of numbers, each number being the magnitude of a relevant boreholeparameter at a point defined by the circumferential direction φ and thedepth z, which method comprises the steps of:

[0006] (a) determining for each point i of the image the slope η_(i) ofthe sinusoids by computing the edge gradient direction;

[0007] (b) selecting a parameter relation (z_(i)=d−R tan Φ cos(φ_(i)−α)) that represents the intersection of a planar event with theborehole wall, wherein the intersection is characterized by threeparameters (Φ, α, d);

[0008] (c) creating a discretized three-dimensional parameter spaceconsisting of numbers as a function of the three parameters (Φ, α, d),wherein each number is a measure of the support for a sinusoid passingthrough (φ_(i), z_(i)) with slope η_(i) characterized by the parametersthat pertain to that number;

[0009] (d) selecting in the parameter space a set of the largestnumbers, wherein the parameters that pertain to each of these largestnumbers represent the intersections of the significant planar eventswith the borehole wall; and

[0010] (e) presenting the intersections pertaining to the set of thelargest numbers as a list of data representing significant planarevents.

[0011] The intersection that pertains to the values for each parameterthat pertain to the significant planar events can be presented to obtaina treated image.

[0012] Steps (c) and (d) of the known method are implemented via aso-called Hough Transformation. Improving the Hough Transformation byusing the edge gradient direction is known from the article‘Generalizing the Hough transform to detect arbitrary shapes’, D. H.Ballard, Pattern Recognition, Vol. 13, No. 2, pages 111-122, 1981.

[0013] In the known method information obtained from the edge gradientdirection is used to further constrain the number of sets of parametersfor which the support has to be evaluated. A disadvantage of the knownmethod is that the edge detector is only capable of detecting the mostprominent local orientation, which is insufficient in case of combinedfractures and bedding or in case of intersecting fractures.

[0014] It is an object of the present invention to provide an improvedmethod that allows distinguishing fractures from bedding and that has animproved signal-to-noise ratio for the detection of fractures.

[0015] To this end the method of detecting significant eventsintersecting a borehole from an image of the borehole wall, which imagecomprises a two-dimensional array of numbers, each number being themagnitude of a relevant borehole parameter at a point defined by thecircumferential direction and the depth, according to the presentinvention comprises the steps of:

[0016] (a) converting the image into a three-dimensional orientationspace consisting of a stack of two-dimensional images, wherein eachtwo-dimensional image is obtained by applying an edge-detecting orline-detecting filter to the borehole image with a particularorientation of the filter;

[0017] (b) selecting a parameter relation that represents theintersection of an event with the borehole wall, wherein theintersection is characterized by n parameters;

[0018] (c) creating an n-dimensional parameter space consisting ofnumbers as a function of the n parameters, wherein each number is ameasure of the support in the orientation space for an intersectioncharacterized by the parameters that pertain to that number;

[0019] (d) selecting in the parameter space a set of the largestnumbers, wherein the parameters that pertain to each of these largestnumbers represent well supported intersections with the borehole wall;and

[0020] (e) presenting the intersections pertaining to the set of thelargest numbers as a list of data representing significant events.

[0021] The intersection that pertains to the values for each parameterthat pertain to the significant events can be presented to obtain atreated image.

[0022] The invention will now be described in more detail by way ofexample with reference to the accompanying drawings, wherein

[0023]FIG. 1 shows schematically an original image obtained with anacoustic borehole imaging tool;

[0024]FIG. 2 shows schematically an orientation space, in which thetrajectories of the support of the sinusoids in FIG. 1 are indicated bycontinuous lines;

[0025]FIG. 3 shows schematically a parameter space; and

[0026]FIG. 4 shows schematically a synthetic image of a borehole wall.

[0027] Reference is now made to FIG. 1. FIG. 1 shows schematically partof an original image of the borehole wall obtained with an acoustictool. The horizontal co-ordinate is the circumferential direction φ andthe vertical co-ordinate is the depth z along the borehole. In FIG. 1three sinusoidal curves are shown, the curves are referred to withreference numerals 3, 5 and 6. The three sinusoidal curves 3, 5 and 6represent intersections that show planar events intersecting theborehole wall. The dashed line 7 represents an artificial sinusoidalcurve that was not present in the original image.

[0028] The graphical representation as shown in FIG. 1 is obtained fromthe two-dimensional array of numbers, each number being the magnitude ofa relevant borehole parameter. In the case of an acoustic tool therelevant borehole parameter is the amplitude of the acoustic pulse thatis reflected on the borehole wall, and in the case of a microresistivitytool the formation resistivity. In the specification and the claims theword ‘image’ is used to refer to an array of numbers and to thegraphical representation of this array.

[0029] The first step of the method of treating this original image isconverting the original image into a three-dimensional orientation spaceconsisting of a stack of two-dimensional images, wherein eachtwo-dimensional image is obtained by applying an edge-detecting orline-detecting filter to the image with a particular orientation of thefilter.

[0030] One way to describe this step mathematically is by using thefollowing equation: I^(OS)(φ, z, ψ)=I(φ, z)*F(φ, z, ψ), wherein I(φ, z)is the magnitude of the relevant borehole parameter in a point (φ, z) ofthe original image as shown in FIG. 1, F(φ, z, ψ) is the transferfunction of the filter rotated over the filter orientation ψ, I^(OS)(φ,z, ψ) is the transformation of the original image in thethree-dimensional orientation space, and I(φ, z)*F(φ, z, ψ) denotes theconvolution of the image and the filter,I(ϕ,  z) * F(ϕ,  z,  ψ) = ∫_(−∞)^(∞)∫_(−∞)^(∞)I(ϕ − ϕ^(′),  z − z^(′))F(ϕ^(′),  z^(′),  ψ)  ϕ^(′)  z^(′).

[0031] The transfer function F(φ, z, ψ) of the filter can be a complexfunction.

[0032] The filter F(φ, z, ψ) is applied to the original image I(φ, z) ateach point (φ, z) of FIG. 1. For a single point 10 in FIG. 1 the filterorientations are shown by means of arrows 12, 13, 14, 15 and 16. Thefilter orientations ψ are 0, π/4, π/2, 3π/4, π, respectively. Here thenumber of filter orientations is five, however, in practice a largenumber of filter orientations is used, for example between 32 and 64.

[0033] The image of FIG. 1 is converted into a three-dimensionalorientation space with co-ordinate axes φ, z and ψ, in which each filterorientation is represented by a plane of constant ψ in the orientationspace.

[0034] An example of the orientation space is shown in FIG. 2. Theintersections of the planes for the filter orientations 12, 13, 14, 15and 16 in FIG. 1 and the z-ψ plane, are referred to by 22, 23, 24, 25and 26. After applying the filter to the sinusoidal curve 3 of FIG. 1, acurve 3′ is obtained in FIG. 2, and the points 30, 31, 32, 33 and 34 onthe curve 3 correspond to the points 30′, 31′, 32′, 33′ and 34′ on thecurve 3′. The curves in the orientation space that correspond to thesinusoidal curves 5 and 6 are curves 5′ and 6′. The points 51, 52, 53and 54 on sinusoidal curve 5 correspond to the points 51′, 52′, 53′ and54′ in the orientation space, and the points 61, 62 and 63 on sinusoidalcurve 6 correspond to the points 61′, 62′ and 63′. It will be understoodthat FIG. 2 is a graphical representation of a three-dimensional arrayof numbers, each number representing the output of the oriented filter.

[0035] Converting the image into a three-dimensional orientation spaceis the essential step of the method of the present invention, becausenow the support for the orientation along the sinusoidal linerepresenting the intersection is taken into account in the subsequentselection of the sinusoids that have most support in the input image.

[0036] The next step of the method according to the present inventioncomprises selecting a parameter relation that represents theintersection of an event with the borehole wall, wherein theintersection is characterized by n parameters.

[0037] In case the event is a planar event, a suitable parameterrelation, that can represent the intersection of the planar event with acylindrical borehole wall is z=d+A sin(φ−α), wherein d, A and α are thethree parameters that define a sinusoidal curve.

[0038] The three parameters d, A and α are now used to define aparameter space, and this parameter space is shown in FIG. 3. A point inthis parameter space corresponds to a particular sinusoidal curve.

[0039] Assume that the artificial sinusoidal curve represented by dashedline 7 in FIG. 1 is characterized by the parameters d₀, A₀ and α₀ thatare the co-ordinates of point 70 in the parameter space shown in FIG. 3.In an analogous way, the sinusoidal curve represented by line 3 in FIG.1 is characterized by the parameters d₁, A₁ and α₁ that are thecoordinates of point 80 in the parameter space shown in FIG. 3. Then thedashed line 7′ in the orientation space of FIG. 2 is the result ofapplying the oriented filter on the sinusoidal curve 7. Summing thenumbers along the curve 7′ in FIG. 2 gives a total number that is ameasure of the support in the orientation space for an intersectioncharacterized by the parameters or co-ordinates that pertain to thatnumber. Thus the number attributed to the point 70 will be lower thanthe number attributed to a point 80 in FIG. 3, wherein the co-ordinatesof point 80 are the parameters of a sinusoidal curve that coincides withcurve 3 in the original image. In conclusion the curve 7 gets lesssupport than the curve 3. In this way a clear distinction is madebetween an artificial curve and an intersection that was present in theoriginal image.

[0040] The numbers can be attributed to the points in the parameterspace in various ways. Summation along a line in orientation space is ageneralized form of the Radon transformation. The generalized Houghtransformation is another possibility.

[0041] The next step of the method according to the present invention isselecting in the parameter space a set of large numbers including thelargest number, wherein the parameters that pertain to each of theselargest numbers represent the significant intersections. This is done bysorting the numbers in descending order, and taking the first m numbers,for example 10 or 100, wherein m depends on a user-provided number.

[0042] The intersection that pertains to the values for each parameterthat pertain to the significant events can be presented. Thispresentation is then a treated image.

[0043] In order to improve the method in dealing with discontinuoussinusoids in the input image, in which case partial sinusoidal eventscan give support to multiple sinusoids in the input image step (d) ofthe method of the present invention suitably further includes some moresteps.

[0044] The first step is selecting k intersections having a high supportto form a set of k candidate intersections and sorting the set bysupport. The parameters that represent the candidate intersection havingthe largest support are stored in an array of intersections.

[0045] Then the data pertaining to the candidate intersection having thelargest support are removed from the orientation space. Having donethat, the support in the orientation space for the remaining candidateintersections is recalculated to obtain a reduced set of candidateintersections, which are sorted by support. The parameters thatrepresent the candidate intersection having the largest support areadded to the array of intersections. It will be understood that if thesupport for an intersection decreases significantly after removing thesupport for a higher ranked candidate intersection, it can be concludedthat the latter intersection shared support with the higher rankedcandidate intersection. The removal and recalculation steps are repeatedfor all candidate intersections to obtain an ordered set ofintersections.

[0046] The last step is selecting from the ordered set of intersectionsa subset of k−i intersections having the largest support, and presentingthe k−i intersections as a list of data representing significant planarevents, wherein i can be any number less than k.

[0047] The number k is suitably in the range of from 10 to 100.

[0048] An illustration of this method is discussed with reference toFIG. 4, which shows schematically a synthetic image of a borehole wall.The solid line 90 and the solid line segments 91, 92 and 93 show wherethere is support for intersections representing relevant planar events.The dotted lines 96, 97 and 98 represent candidate intersections havingthe largest support. The ordered set of intersections will have thesequence 96, 97 and 98. Selecting two (i=1) intersections out of thethree (k=3), will allow discarding the intersection numbered 98.

[0049] When the image contains noise, there is support for a largenumber of curves representing intersections. In order to reduce theeffect of noise, step (d) of the method of the present inventionsuitably further comprises a method to re-evaluate candidate events bydetermining whether they are supported by edges or lines in the originalimage that have a sufficiently narrow range of orientations. Theexpressions candidate events and candidate intersections are usedsynonymously in the specification and in the claims.

[0050] A suitable way of doing this comprises determining for everypoint in the orientation space that belongs to a well-supportedcandidate intersection a support set comprising those orientations forwhich the support is larger than a threshold value times the support ofactual orientation of the well-supported candidate intersection; andremoving the candidate intersection from the list of candidateintersections if the number of elements in the support set is relativelylarge compared to the number of filter orientations. The threshold valueT is less than 1, for example 0.8. Thus, only those points on thetrajectory are taken into account for which the support set is asufficiently small fraction of the number of filter orientations.

[0051] The filter F(φ, z, ψ) is suitably a filter, of which the FourierTransform is the product of three factors: F_(T)(ω, θ, ψ)=G_(r)(ω,ω_(c), σ_(r))G_(a)(θ−ψ, N)Q(θ−ψ), wherein G_(r) is the radial part ofthe filter, G_(a) is the angular part of the filter and Q is thequadrature factor. The factor Q ensures that the filter is a quadraturefilter, which is a filter wherein the phase difference between tworesponses is π/2.

[0052] The radial part of the filter is given by the following equation:${G_{r}\left( {\omega,\quad \omega_{c},\quad \sigma_{r}} \right)} = {\left( \frac{\omega}{\omega_{c}} \right)^{({\omega_{c}^{2}/\sigma_{r}^{2}})}{{\exp \left( {- \frac{\omega^{2} - \omega_{c}^{2}}{2\sigma_{r}^{2}}} \right)}.}}$

[0053] The radial part of the filter selects a non-symmetric frequencyband around ω_(c) having a width of σ_(r).

[0054] The angular part of the filter is given by the followingequation:${{G_{a}\left( {\theta - {\psi,\quad N}} \right)} = {{\exp \left( {- \frac{{N^{2}\left( {\theta - \psi} \right)}^{2}}{2\pi^{2}}} \right)},}}\quad$

[0055] wherein N is the number of filter orientations.

[0056] The factor Q ensures that the filter is a quadrature filter andis given by the following equation: Q(θ−ψ)=1 for −(π/2)<(θ−ψ)<(π/2),Q(θ−ψ)=0 for −π<(θ−ψ)<−(π/2) and Q(θ−ψ)=0 for (π/2)<(θ−ψ)<π.

[0057] In the spatial domain, the real part of the filter F(φ, z, ψ) issensitive to even signals (lines) and the imaginary part is sensitive toodd signals (edges). If so required, the user can select to make thefracture detection sensitive to line or step edges only by selecting thereal or imaginary part of the filter output, rather than the absolutevalue.

[0058] When the output of the oriented filter is a complex number, thenumbers in the orientation space are the absolute value of the complexnumber, |I^(OS)(φ, z, ψ)|.

[0059] It will be understood that other edge or line detecting filterscan also be used.

[0060] An advantage of the method of the present invention is thatmultiple oriented structures can be detected. Furthermore, the method ofthe present invention is less sensitive to noise than the known methods.

1. Method of detecting significant events intersecting a borehole froman image of the borehole wall, which image comprises a two-dimensionalarray of numbers, each number being the magnitude of a relevant boreholeparameter at a point defined by the circumferential direction and thedepth, which method comprises the steps of: (a) converting the imageinto a three-dimensional orientation space consisting of a stack oftwo-dimensional images, wherein each two-dimensional image is obtainedby applying an edge-detecting or line-detecting filter to the image witha particular orientation of the filter; (b) selecting a parameterrelation that represents the intersection of an event with the boreholewall, wherein the intersection is characterized by n parameters; (c)creating an n-dimensional parameter space consisting of numbers as afunction of the n parameters, wherein each number is a measure of thesupport in the orientation space for an intersection characterized bythe parameters that pertain to that number; (d) selecting in theparameter space a set of the largest numbers, wherein the parametersthat pertain to each of these largest numbers represent well supportedintersections with the borehole wall; and (e) presenting theintersections pertaining to the set of the largest numbers as a list ofdata representing significant events.
 2. Method according to claim 1,wherein step (d) further includes the steps of: d1) selecting kintersections having a high support to form a set of k candidateintersections and sorting the set by support; d2) storing the parametersthat represent the candidate intersection having the largest support inan array of intersections; d3) removing the data pertaining to thecandidate intersection having the largest support from the orientationspace; d4) recalculating the support in the orientation space for theremaining candidate intersections to obtain a reduced set of candidateintersections, sorting the reduced set by support, and adding theparameters that represent the candidate intersection having the largestsupport to the array of intersections; d5) repeating steps d3) and d4)for all candidate intersections to obtain an ordered set ofintersections; and d6) selecting from the ordered set of intersectionsthe k−i intersections having the largest support, and presenting the k−iintersections as a list of data representing significant events, whereini can be any number less than k.
 3. Method according to claims 1 and 2,wherein step (d) further comprises determining for every point in theorientation space that belongs to a well-supported candidateintersection a support set comprising those orientations for which thesupport is larger than a threshold value times the support of actualorientation of the well-supported candidate intersection; and removingthe candidate intersection from the list of candidate intersections ifthe number of elements in the support set is relatively large comparedto the number of filter orientations.